I'm trying to see near which points of R^3 I can solve for theta, phi, and rho in terms of x,y, and z. I know i need to find the determinant and see when it equals zero; however, I get the determinant to equal zero when sin(phi) = 0, and when tan(theta) = -cot(phi). The first is right, but i've checked my work many times and keep getting the last solution. I just calculated the determinant of the partial derivatives (dx/dtheta, dx / dphi, dx / drho...dy/dtheta, dy/dphi, dy/drho...dz/dtheta, dz/dphi, dz/drho). I've checked my work many times. Am I correct, or am I doing something wrong?